where \(p_X(\mathbf {x})\)  is the input signal probability density function (PDF), \(X\)  is the channel input signal and \(Y\)  is the channel output signal and \(I(X;Y)\)  is the mutual information between \(X\)  and \(Y\) .
However, estimating the channel capacity is a challenging task and few special cases, such as the additive white Gaussian noise (AWGN) channel case, have been solved so far [1]}.
When the channel is not AWGN, the analytic study becomes mostly intractable leading to numerical solutions, relaxations or lower and upper bounds [2]}.
We argue that a data-driven approach can be pursued to learn the channel capacity. In the following we develop a cooperative framework aiming at estimating the capacity of a generic memory-less vector channel. In particular, we firstly propose two discriminative mutual information estimators, indirect and direct, based on adversarial training objectives. Secondly, we exploit the direct estimator to solve the channel capacity estimation problem, seen as a cooperative game between a generator and a discriminator. Lastly, we establish a connection to other variational lower bounds.
